What is an Elevation Grade Calculator?
An elevation grade calculator converts a vertical rise and horizontal run into the slope's steepness expressed several ways: as a grade percentage, as an angle in degrees, as the true slope (hypotenuse) length, and as a run-to-rise ratio. Grade is widely used for roads, railways, driveways, ramps, hiking trails, and drainage design. This tool is unit-agnostic—use feet, meters, or any unit, as long as rise and run share the same unit.
How to Use It
Enter the rise (the change in elevation) and the run (the horizontal distance covered). Press calculate to instantly see the grade as a percent, the incline angle, the diagonal slope length, and the ratio. For example, a road that climbs 10 feet over 100 feet of horizontal distance has a 10% grade.
The Formula Explained
The grade percentage is simply \(\frac{\text{rise}}{\text{run}} \times 100\). The angle is found with the inverse tangent:
$$\text{angle} = \tan^{-1}\!\left(\frac{\text{rise}}{\text{run}}\right) \times \frac{180}{\pi}$$converting radians to degrees. The slope length—the actual distance you travel along the incline—uses the Pythagorean theorem: \(\sqrt{\text{rise}^2 + \text{run}^2}\).
Worked Example
Suppose a trail rises 30 meters over a horizontal run of 40 meters.
$$\text{Grade} = \frac{30}{40} \times 100 = \mathbf{75\%}$$$$\text{Angle} = \tan^{-1}\!\left(\frac{30}{40}\right) = \tan^{-1}(0.75) \approx \mathbf{36.87°}$$$$\text{Slope length} = \sqrt{30^2 + 40^2} = \sqrt{900 + 1600} = \sqrt{2500} = \mathbf{50 \text{ m}}$$$$\text{Ratio} = \frac{40}{30} \approx \mathbf{1.33 : 1}$$
FAQ
What's the difference between grade and angle? Grade is a percentage (rise ÷ run × 100), while angle is measured in degrees. A 100% grade equals 45°, not 90°.
Can grade exceed 100%? Yes. A grade over 100% simply means the rise is greater than the run, i.e. the angle is steeper than 45°.
What units should I use? Any units work as long as rise and run use the same one, because grade is a ratio.
